Homework 5
Solutions
Exercise 1. A particle is moved along the x-axis by a force that measures 10/(1 + x)2
pounds at a point x feet from the origin. Find the work done in moving the particle from
the origin to a distance of 9 feet.
Exercise 2. A circular swimming pool has a diameter of 24 ft, the sides are 5 ft high,
and the depth of the water is 4 ft. How much work is required to pump all of the water
out over the side? (Use the fact that water weighs 62.5 lb/ft3 .)
Exercise 3. Sketch the region bounded by the given curves and find its center of mass.
√
1. y = x, y = x
1
2. y = x + 2,
3. y = sin x,
y = x2
y = cos x,
x = 0,
, x = π/4
2
Exercise 4. Find the length of the curve
1. y = 1 + 6x3/2 ,
0≤x≤1
2. y = ln(cos x),
0 ≤ x ≤ π/3
3. x =
1√
3 y(y
− 3),
1≤y≤9
3